SME
Grade 12 Math · Problem type
A matrix times a vector
Use this for “Multiply [[2, 1], [3, 4]] by the column (5, −1).”
Diagram
A is 2 × 2 and B is 2 × 1, so AB is 2 × 1.
Row 1 of A times column 1 of B gives entry (1, 1): c₁₁ = 2 × 5 + 1 × (−1) = 9.
Tap an entry of AB to see its row and column.
This is an example. Type your own values to start a new problem.
=
Formulas
p
=
a
×
x
+
b
×
y
9 = 2 × 5 + 1 × (−1)
q
=
c
×
x
+
d
×
y
11 = 3 × 5 + 4 × (−1)
Assumptions
•
Each row of the matrix times the column gives one entry: across the row, down the column.
•
The matrix must have as many columns as the vector has rows.
Step-by-step
WE KNOW
a = 2, b = 1, c = 3, d = 4, x = 5, y = −1
FIND
answer, top (p), answer, bottom (q)
Step 1 · Find answer, top (p)
Use p = a × x + b × y
Row 1 times the column: multiply entry by entry, then add.
p
=
2
×
5
+
1
×
(−1)
p
=
10
−
1
p
=
9
Step 2 · Find answer, bottom (q)
Use q = c × x + d × y
Row 2 times the column: multiply entry by entry, then add.
q
=
3
×
5
+
4
×
(−1)
q
=
15
−
4
q
=
11
Check
Put the numbers back in. Both sides should match.
9 = 2 × 5 + 1 × (−1) ✓
11 = 3 × 5 + 4 × (−1) ✓
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